Displacement analytical solution of a deep tunnel with arbitrary cross section in transversely isotropic rock mass

Sedimentary rock with layered structure accounts for 2/3 of global land area, and lots of metamorphic rock also has significant features of layered structure, so there are many stability problems about layered rock mass in geotechnical engineering. Layered rock mass is generally considered to be transversely isotropic solid. Based on the complex variable expression of stress function, the complex variable expression of displacement components of transversely isotropy is deduced; the displacement analytical solution of a deep tunnel with arbitrary cross section in transversely isotropic rock mass is derived by conformal mapping method. Although the cross section of the tunnel is assumed to be parallel to the isotropic plane, the displacement analytical solution indicates that radial displacement of surrounding rock is related not only to elastic modulus and poisson ratio on the isotropic plane but also to that in the direction normal to the isotropic plane.